Ambiguity resolution from the phase measurement in distance estimation based on radio frequency signals

ABSTRACT

A system is provided for resolving ambiguity in a phase measurement used in a distance estimation for an object. The system includes a transmitter for transmitting RF signals from an object location. The system includes measurement equipment for receiving the transmitted RF signals as corresponding received RF signals and measuring a plurality of phases at different frequencies between the transmitted RF signals and the corresponding received RF signals. The system includes a processor. The processor is configured to calculate normalized phases from the plurality of measured phases. The processor is configured to perform an intra-frequency ambiguity resolution process that resolves an ambiguity for the normalized phases for a single frequency using an ambiguity factor. The processor is configured to perform an inter-frequency ambiguity resolution process that resolves an ambiguity for the normalized phases across multiple tones using a characteristic curve to provide a resolved phase measurement for the distance estimation.

RELATED APPLICATION INFORMATION

This application claims priority to provisional application Ser. No.62/463,774, filed on Feb. 27, 2017, incorporated herein by reference.This application is related to an application 15/891,800 entitled“Distance Estimation Using Phase Information”, and which is incorporatedby reference herein in its entirety. This application is related to anapplication 15/891,906 entitled “Distance Estimation Using MultiplePhase Differences”, and which is incorporated by reference herein in itsentirety. This application is related to an application 15/891,994entitled “Distance Estimation Between an RFID Tag and an RFID Reader”,and which is incorporated by reference herein in its entirety.

BACKGROUND Technical Field

The present invention relates to distance estimation, and moreparticularly to ambiguity resolution from the phase measurement indistance estimation based on radio frequency signals.

Description of the Related Art

The problem of estimating the distance between two objects has many usecases depending on the accuracy of the estimation. A telemetricinstrument using laser beams enables applications that do not requirehigh accuracy such as land surveying. On the other hand, laser devicescan be used for professional sports (centimeter accuracy) and tooltuning where sub-millimeter accuracy is required.

One particular class of sensor-based distance estimation is RF-based(radio frequency based) distance estimation. RF-based distanceestimation and ultrasonic (sound-based) measurement have been around fordecades and were used primarily in radar/sonar applications. The mainidea is to estimate the time-of-flight for the wave that is travelingbetween two end points, e.g., a fixed measurement point to an object ofinterest. Given the speed of the wave in a particular medium between thetwo end points, the distance is found by the knowledge of thetime-of-flight. However, for small distances, the time-of-flight for RFwaves is very small and it is not possible to simply find it by simpletransmission of a pulse and detection of the time between thetransmission and reception of the pulse. Moreover, in most of the bands,the RF-signal may pass though different media, and get absorbed orreflected from objects. Hence, the received signal usually has multiplecopies of the transmitted signal with different gain and phases that aredistorted by non-flat fading. These challenges make the problem ofRF-based distance estimation challenging.

Accordingly, there is a need for a solution to the aforementioned ofestimating the distance between two objects, particularly for the caseof RF-based distance estimation.

SUMMARY

According to an aspect of the present invention, a system is providedfor resolving ambiguity in a phase measurement used in a distanceestimation for an object. The system includes a transmitter fortransmitting RF signals from a location of the object. The systemfurther includes measurement equipment, including a receiver, forreceiving the transmitted RF signals as corresponding received RFsignals and measuring a plurality of phases at different frequenciesbetween the transmitted RF signals and the corresponding received RFsignals. The system also includes a processor. The processor isconfigured to calculate normalized phases from the plurality of measuredphases. The processor is further configured to perform anintra-frequency ambiguity resolution process that resolves an ambiguityfor the normalized phases for a single frequency using an ambiguityfactor. The processor is also configured to perform an inter-frequencyambiguity resolution process that resolves an ambiguity for thenormalized phases across a plurality of tones using a characteristiccurve to provide a resolved phase measurement for the distanceestimation for the object.

According to another aspect of the present invention, acomputer-implemented method is provided for resolving ambiguity in aphase measurement used in a distance estimation for an object. Themethod includes measuring, by measurement equipment, a plurality ofphases at different frequencies between transmitted Radio Frequency (RF)signals from a location of the object and corresponding received RFsignals at the measurement equipment. The method further includescalculating, by a processor, normalized phases from the plurality ofmeasured phases. The method also includes performing, by the processor,an intra-frequency ambiguity resolution process that resolves anambiguity for the normalized phases for a single frequency using anambiguity factor. The method additionally includes performing, by theprocessor, an inter-frequency ambiguity resolution process that resolvesan ambiguity for the normalized phases across a plurality of tones usinga characteristic curve to provide a resolved phase measurement for thedistance estimation for the object.

According to yet another aspect of the present invention, a computerprogram product is provided for resolving ambiguity in a phasemeasurement used in a distance estimation for an object. The computerprogram product includes a non-transitory computer readable storagemedium having program instructions embodied therewith. The programinstructions are executable by a computer to cause the computer toperform a method. The method includes measuring, by measurementequipment, a plurality of phase differences at different frequenciesbetween transmitted Radio Frequency (RF) signals from a location of theobject and corresponding received RF signals at the measurementequipment. The method further includes calculating, by a processor,normalized phases from the measured phases. The method also includesperforming, by the processor, an intra-frequency ambiguity resolutionprocess that resolves an ambiguity for the normalized phases for asingle frequency using an ambiguity factor. The method additionallyincludes performing, by the processor, an inter-frequency ambiguityresolution process that resolves an ambiguity for the normalized phasesacross a plurality of tones using a characteristic curve to provide aresolved phase measurement for the distance estimation for the object.

These and other features and advantages will become apparent from thefollowing detailed description of illustrative embodiments thereof,which is to be read in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

The disclosure will provide details in the following description ofpreferred embodiments with reference to the following figures wherein:

FIG. 1 shows an exemplary system for ambiguity resolution from the phasemeasurement in distance estimation based on radio frequency signals, inaccordance with an embodiment of the present principles;

FIG. 2 shows an exemplary system for distance estimation using multiplephase differences, in accordance with an embodiment of the presentinvention;

FIG. 3 shows an exemplary system for distance estimation using phaseinformation, in accordance with an embodiment of the present invention;

FIG. 4 shows an exemplary system for distance estimation between an RFIDtag and an RFID reader, in accordance with an embodiment of the presentinvention;

FIG. 5 shows an exemplary processing system to which the presentprinciples may be applied, according to an embodiment of the presentprinciples;

FIG. 6 shows an exemplary method for distance estimation using phaseinformation, in accordance with an embodiment of the present principles;

FIG. 7 shows an exemplary method for distance estimation using multiplephase differences, in accordance with an embodiment of the presentprinciples;

FIG. 8 shows an exemplary method for ambiguity resolution from the phasemeasurement in distance estimation based on radio frequency signals, inaccordance with an embodiment of the present principles; and

FIG. 9 shows an exemplary method for distance estimation between an RFIDtag and an RFID reader, in accordance with an embodiment of the presentprinciples.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

The present invention is directed to ambiguity resolution from the phasemeasurement in distance estimation based on radio frequency signals.

It is to be appreciated that recognition in distance estimation usingphase information in accordance with the present invention can beapplied to applications including, but not limited to, any of thefollowing: distance estimation using multiple phase differences;ambiguity resolution from the phase measurement in distance estimationbased on radio frequency signals; and distance estimation between anRFID tag and an RFID reader; and so forth. Of course, the presentinvention can also be applied to a myriad of other applications, asreadily appreciated by one of ordinary skill in the art given theteachings of the present invention provided herein, while maintainingthe spirit of the present invention.

FIG. 1 shows an exemplary system 100 for ambiguity resolution from thephase measurement in distance estimation based on radio frequencysignals, in accordance with an embodiment of the present principles.

The system 100 includes a Radio Frequency (RF) transmitter 110, a RFreceiver 120, phase measurement equipment (interchangeably referred toherein as “measurement equipment” or “ME”) 130, and at least onecomputing device 140. In an embodiment, the system 100 can furtherinclude a display device 150.

The RF transmitter 110 includes a set 110A of one or more antennas, andthe RF receiver 120 includes a set 120A of one or more antennas.

In an embodiment, the at least one computing device 140 is forcontrolling operations of one or more of the RF transmitter 110, the RFreceiver 120, and the phase measurement equipment 130. Communicationsbetween the RF transmitter 110 and the measurement equipment 130 are nowshown in FIG. 1 for the sake of clarity. However, any communicationtechnology can be used between the elements of system 100, whilemaintaining the spirit of the present invention. In an embodiment, theat least one computing device 140 can be a processor-based device suchas, for example, but not limited to, a controller, a server, and soforth. In an embodiment, the at least one computing device 140 is partof the measurement equipment 130. In another embodiment, the at leastone computing device 140 is a separate device from the measurementequipment 130 that is operatively coupled to, and located at a samelocation as, the measurement equipment 130.

The system 100 is applied to an object 199 (interchangeably referred toherein as “OBJ”) whose distance is to be measured from a referencepoint. The system 100 is configured to resolve ambiguity from phasemeasurements in distance estimation based on Radio Frequency (RF)signals. In the embodiment of FIG. 1, the measurement equipment 130 andthe receiver 120 are located at the same location. Hence, the referencepoint can be considered to be the (common) location of the measurementequipment 130 or the receiver 120, such that the distance measurementcan be considered to span the distance from the object to any of themeasurement equipment 130 or the receiver 120 given their commonlocation.

The at least one computing device 140 is configured to perform distanceestimation using phase information. To that end, the transmitter 110transmits RF signals from a location of the object 199. The receiver 120receives the transmitted RF signals as corresponding received RFsignals. The measurement equipment 130 measures a plurality of phases atdifferent frequencies between the transmitted RF signals and thecorresponding received RF signals.

The at least one computing device 140 is operatively coupled to themeasurement equipment 130 and is configured to calculate normalizedphases from the plurality of measured phases, perform an intra-frequencyambiguity resolution process that resolves an ambiguity for thenormalized phases for a single frequency using an ambiguity factor, andperform an inter-frequency ambiguity resolution process that resolves anambiguity for the normalized phases across a plurality of tones using acharacteristic curve to provide a resolved phase measurement for thedistance estimation for the object. In an embodiment, the at least onecomputing device 140 can be configured to provide an updated distanceestimation based on the resolved phase measurement.

In an embodiment, the display device 150 is operatively coupled to theat least one computing device 140 and is configured to display theestimate of the distance. In this way, an estimate of the distance fromthe receiver 120 or ME 130 is estimated using phase information andprovided to a user.

FIG. 2 shows an exemplary system 200 for distance estimation usingmultiple phase differences, in accordance with an embodiment of thepresent invention.

The system 200 includes a Radio Frequency (RF) transmitter 210, a RFreceiver 220, phase measurement equipment (interchangeably referred toherein as “measurement equipment” or “ME”) 230, and at least onecomputing device 240. In an embodiment, the system 200 can furtherinclude a display device 250.

The RF transmitter 210 includes a set 210A of one or more antennas, andthe RF receiver 220 includes a set 220A of one or more antennas.

In an embodiment, the at least one computing device 240 is forcontrolling operations of one or more of the RF transmitter 210, the RFreceiver 220, and the phase measurement equipment 230. Communicationsbetween the RF transmitter 210 and the measurement equipment 230 are nowshown in FIG. 2 for the sake of clarity. However, any communicationtechnology can be used between the elements of system 200, whilemaintaining the spirit of the present invention. In an embodiment, theat least one computing device 240 can be a processor-based device suchas, for example, but not limited to, a controller, a server, and soforth. In an embodiment, the at least one computing device 240 is partof the measurement equipment 230. In another embodiment, the at leastone computing device 240 is a separate device from the measurementequipment 230 that is operatively coupled to, and located at a samelocation as, the measurement equipment 230.

The system 200 is applied to an object 299 (interchangeably referred toherein as “OBJ”) whose distance is to be measured from a referencepoint. In the embodiment of FIG. 2, the measurement equipment 230 andthe receiver 220 are located at the same location. Hence, the referencepoint can be considered to be the (common) location of the measurementequipment 230 or the receiver 220, such that the distance measurementcan be considered to span the distance from the object to any of themeasurement equipment 230 or the receiver 220 given their commonlocation.

The at least one computing device 240 is configured to perform distanceestimation using multiple phase differences. To that end, thetransmitter 210 transmits RF signals from a location of the object 299.The receiver 220 receives the transmitted RF signals as correspondingreceived RF signals. The measurement equipment 230 measures a pluralityof phase differences at different frequencies between the transmitted RFsignals and the corresponding received RF signals.

The at least one computing device 240 is operatively coupled to themeasurement equipment 230 and is configured to calculate correctedphases by resolving one or more ambiguities from the plurality of phasedifferences, obtain a characteristic curve using the corrected phases,and provide an estimate of the distance based on the characteristiccurve and the corrected phases.

In an embodiment, the display device 250 is operatively coupled to theat least one computing device 240 and is configured to display theestimate of the distance. In this way, an estimate of the distance fromthe receiver 220 or ME 230 is estimated using multiple phase differencesand provided to a user.

FIG. 3 shows an exemplary system 300 for distance estimation using phaseinformation, in accordance with an embodiment of the present invention.

The system 300 includes a Radio Frequency (RF) transmitter 310, a RFreceiver 320, phase measurement equipment (interchangeably referred toherein as “measurement equipment” or “ME”) 330, and at least onecomputing device 340. In an embodiment, the system 300 can furtherinclude a display device 350.

The RF transmitter 310 includes a set 310A of one or more antennas, andthe RF receiver 320 includes a set 320A of one or more antennas.

In an embodiment, the at least one computing device 340 is forcontrolling operations of one or more of the RF transmitter 310, the RFreceiver 320, and the phase measurement equipment 330. Communicationsbetween the RF transmitter 310 and the measurement equipment 330 are nowshown in FIG. 3 for the sake of clarity. However, any communicationtechnology can be used between the elements of system 300, whilemaintaining the spirit of the present invention. In an embodiment, theat least one computing device 340 can be a processor-based device suchas, for example, but not limited to, a controller, a server, and soforth. In an embodiment, the at least one computing device 340 is partof the measurement equipment 330. In another embodiment, the at leastone computing device 340 is a separate device from the measurementequipment 330 that is operatively coupled to, and located at a samelocation as, the measurement equipment 330.

The system 300 is applied to an object 399 (interchangeably referred toherein as “OBJ”) whose distance is to be measured from a referencepoint. In the embodiment of FIG. 3, the measurement equipment 330 andthe receiver 320 are located at the same location. Hence, the referencepoint can be considered to be the (common) location of the measurementequipment 330 or the receiver 320, such that the distance measurementcan be considered to span the distance from the object to any of themeasurement equipment 330 or the receiver 320 given their commonlocation.

For the sake of clarity, a definition of some of the terms used hereinwill now be given. As used herein, the terms “measured phase” and“differential phase” interchangeably refer to the difference between thephases of the backscattered (or received) signal and the transmittedsignal. Moreover, as used herein, the term “normalized phase” refers toa scaled version of the differential phase in order to convert thedifferential phase into a different range, e.g., [0,1] instead of [0, 2\pi]. The normalized phase can also be used to change the dimension ofthe differential phase. For example to transform the differential phaseinto a distance that is a fraction of the waveform which is equivalentto that differential phase.

The at least one computing device 340 is configured to perform distanceestimation using phase information. To that end, the transmitter 310transmits RF signals 310B from a location of the object 399. Thereceiver 320 receives the transmitted RF signals as correspondingreceived RF signals 320B. The measurement equipment 330 measures aplurality of phase differences at different frequencies between thetransmitted RF signals and the corresponding received RF signals.

The at least one computing device 340 is operatively coupled to themeasurement equipment 330 and is configured to calculate normalizedphases from the plurality of phase differences, calculate correctedphases by resolving one or more ambiguities from the normalized phases,obtain a characteristic curve using the corrected phases, and provide anestimate of the distance based on the characteristic curve and thecorrected phases.

In an embodiment, the display device 350 is operatively coupled to theat least one computing device 340 and is configured to display theestimate of the distance. In this way, an estimate of the distance fromthe receiver 320 or ME 330 is estimated using phase information andprovided to a user.

FIG. 4 shows an exemplary system 400 for distance estimation between anRFID tag and an RFID reader, in accordance with an embodiment of thepresent invention.

The system 400 includes a Radio Frequency Identifier (RFID) reader 410,a RFID tag 420, phase measurement equipment (interchangeably referred toherein as “measurement equipment” or “ME”) 430, and at least onecomputing device 440. In an embodiment, the system 400 can furtherinclude a display device 450.

The RFID reader 410 includes a set 410A of one or more antennas, and theRF tag 420 includes a set 420A of one or more antennas.

In an embodiment, the at least one computing device 440 is forcontrolling operations of one or more of the RF reader 410, the RF tag420, and the phase measurement equipment 430. Communications between theRF reader 410 and the measurement equipment 430 are now shown in FIG. 4for the sake of clarity. However, any communication technology can beused between the elements of system 400, while maintaining the spirit ofthe present invention. In an embodiment, the at least one computingdevice 440 can be a processor-based device such as, for example, but notlimited to, a controller, a server, and so forth. In an embodiment, theat least one computing device 440 is part of the measurement equipment430. In another embodiment, the at least one computing device 440 is aseparate device from the measurement equipment 430 that is operativelycoupled to, and located at a same location as, the measurement equipment430.

The system 400 is applied to the RFID tag 420 (interchangeably referredto herein as “OBJ”) whose distance is to be measured from a referencepoint. In an embodiment, the system can be applied to an object 499attached to the RFID tag, wherein the attached object can beinterchangeably referred to herein as “OBJ”, as opposed to the RFID tag.In the embodiment of FIG. 4, the measurement equipment 430 and the RFIDreader 420 are located at the same location. Hence, the reference pointcan be considered to be the (common) location of the measurementequipment 430 or the RFID reader 420, such that the distance measurementcan be considered to span the distance from the object to any of themeasurement equipment 430 or the RFID reader 420 given their commonlocation.

The measurement equipment 430 is configured to measure a plurality ofphase differences at different frequencies between transmitted RadioFrequency (RF) signals from the RFID reader 420 and correspondingreceived RF signals at the RFID tag 410.

The at least one computing device 440 is configured to calculatenormalized phases from the plurality of phase differences, calculatecorrected phases by resolving one or more ambiguities from thenormalized phases, obtain a characteristic curve using the correctedphases, and provide an estimate of the distance based on thecharacteristic curve and the corrected phases.

Further regarding the systems 100, 200, 300, and 400 of FIGS. 1, 2, 3,and 4, respectively, it is to be appreciated that while some of theconstituent elements thereof are shown as separate elements, in otherembodiments, one or more elements can be combined. For example, thereceiver can be part of the ME, the ME can be part of the at least onecomputing device, the transmitted can be part of the ME, and so forth.These and other variations and configurations of the elements of systems100, 200, 300, and 400 are readily determined by one of ordinary skillin the art given the teachings of the present invention provided herein,while maintaining the spirit of the present invention.

FIG. 5 shows an exemplary processing system 500 to which the presentprinciples may be applied, according to an embodiment of the presentprinciples. In an embodiment, the at least one computing device 140 ofFIG. 1, the at least one computing device 240 of FIG. 2, the at leastone computing device 340 of FIG. 3, and the at least one computingdevice 440 of FIG. 4 can be implemented, at least in part, by processingsystem 500.

The processing system 500 includes at least one processor (CPU) 504operatively coupled to other components via a system bus 502. A cache506, a Read Only Memory (ROM) 508, a Random Access Memory (RAM) 510, aninput/output (I/O) adapter 520, a sound adapter 530, a network adapter540, a user interface adapter 550, and a display adapter 560, areoperatively coupled to the system bus 502. The processing system 500further includes at least one Graphics Processing Unit (GPU) 592.

A first storage device 522 and a second storage device 524 areoperatively coupled to system bus 502 by the I/O adapter 520. Thestorage devices 522 and 524 can be any of a disk storage device (e.g., amagnetic or optical disk storage device), a solid state magnetic device,and so forth. The storage devices 522 and 524 can be the same type ofstorage device or different types of storage devices.

A speaker 532 is operatively coupled to system bus 502 by the soundadapter 530. A transceiver 542 is operatively coupled to system bus 502by network adapter 540. A display device 562 is operatively coupled tosystem bus 502 by display adapter 560.

A first user input device 552, a second user input device 554, and athird user input device 556 are operatively coupled to system bus 502 byuser interface adapter 550. The user input devices 552, 554, and 556 canbe any of a keyboard, a mouse, a keypad, an image capture device, amotion sensing device, a microphone, a device incorporating thefunctionality of at least two of the preceding devices, and so forth. Ofcourse, other types of input devices can also be used, while maintainingthe spirit of the present principles. The user input devices 552, 554,and 556 can be the same type of user input device or different types ofuser input devices. The user input devices 552, 554, and 556 are used toinput and output information to and from system 500.

Of course, the processing system 500 may also include other elements(not shown), as readily contemplated by one of skill in the art, as wellas omit certain elements. For example, various other input devicesand/or output devices can be included in processing system 500,depending upon the particular implementation of the same, as readilyunderstood by one of ordinary skill in the art. For example, varioustypes of wireless and/or wired input and/or output devices can be used.Moreover, additional processors, controllers, memories, and so forth, invarious configurations can also be utilized as readily appreciated byone of ordinary skill in the art. These and other variations of theprocessing system 500 are readily contemplated by one of ordinary skillin the art given the teachings of the present principles providedherein.

Moreover, it is to be appreciated that systems 100, 200, 300, and 400described above with respect to FIGS. 1, 2, 4, and 4, respectively, aresystems for implementing respective embodiments of the presentprinciples. Part or all of processing system 500 may be implemented inone or more of the elements of any of systems 100, 200, 300, and 400.

Further, it is to be appreciated that system 500 may perform at leastpart of the methods described herein including, for example, at leastpart of method 600 of FIG. 6 and/or at least part of method 700 of FIG.7, and/or at least part of method 800 of FIG. 8 and/or at least part ofmethod 900 of FIG. 9. Similarly, part or all of any of systems 100, 200,300, and/or 400 may be used to perform at least part of method 600 ofFIG. 6 and/or at least part of method 700 of FIG. 7, and/or at leastpart of method 800 of FIG. 8 and/or at least part of method 900 of FIG.9.

FIG. 6 shows an exemplary method 600 for distance estimation using phaseinformation, in accordance with an embodiment of the present principles.In an embodiment, the method 600 can be used to estimate the distancebetween an object and measurement equipment using phase information. Inan embodiment, the method 600 of FIG. 6 is performed by, e.g., system100 of FIG. 1.

At block 610, measure, by the measurement equipment, a plurality ofphase differences at different frequencies between transmitted RadioFrequency (RF) signals from a location of the object and correspondingreceived RF signals at the measurement equipment.

At block 620, calculate, by the at least one computing device,normalized phases from the plurality of phase differences.

At block 630, calculate, by the at least one computing device, correctedphases by resolving one or more ambiguities from the normalized phases.

At block 640, obtain, by the at least one computing device, acharacteristic curve using the corrected phases.

At block 650, provide, by the at least one computing device, an estimateof the distance based on the characteristic curve and the correctedphases.

In an embodiment, block 650 can include block 650A.

At block 650A, display, by a display device, the estimate of thedistance.

At block 660, perform one or more actions based on the estimate of thedistance. For example, the one or more actions can be directed to one ormore of the following: object tracking; an Advanced Driver-AssistanceSystem (ADAS); surveillance; and so forth.

FIG. 7 shows an exemplary method 700 for distance estimation usingmultiple phase differences, in accordance with an embodiment of thepresent principles. In an embodiment, the method 600 can be used toestimate the distance between an object and measurement equipment usingmultiple phase differences. In an embodiment, the method 700 of FIG. 7is performed by, e.g., system 200 of FIG. 2.

At block 710, measure, by the measurement equipment, a plurality ofphase differences at different frequencies between transmitted RadioFrequency (RF) signals from a location of the object and correspondingreceived RF signals at a receiver coupled to the measurement equipment.

At block 720, calculate, by the at least one computing device, correctedphases by resolving one or more ambiguities from the plurality of phasedifferences.

At block 730, obtain, by the at least one computing device, acharacteristic curve using the corrected phases.

At block 740, provide, by the at least one computing device, an estimateof the distance based on the characteristic curve and the correctedphases.

In an embodiment, block 740 can include block 740A.

At block 740A, display, by a display device, the estimate of thedistance.

At block 750, perform one or more actions based on the estimate of thedistance. For example, the one or more actions can be directed to one ormore of the following: object tracking; an Advanced Driver-AssistanceSystem (ADAS); surveillance; and so forth.

FIG. 8 shows an exemplary method 800 for ambiguity resolution from thephase measurement in distance estimation based on radio frequencysignals, in accordance with an embodiment of the present principles. Inan embodiment, the method 800 can be used for ambiguity resolution in adistance estimation relating to the distance between an object andmeasurement equipment. In an embodiment, the method 800 of FIG. 8 isperformed by, e.g., system 300 of FIG. 3.

At block 810, measure, by measurement equipment, a plurality of phasesat different frequencies between transmitted Radio Frequency (RF)signals from a location of the object and corresponding received RFsignals at the measurement equipment.

At block 820, calculate, by the at least one computing device,normalized phases from the plurality of measured phases.

At block 830, perform, by the at least one computing device, anintra-frequency ambiguity resolution process that resolves an ambiguityfor the normalized phases for a single frequency using an ambiguityfactor.

At block 840, perform, by the at least one computing device, aninter-frequency ambiguity resolution process that resolves an ambiguityfor the normalized phases across a plurality of tones using acharacteristic curve to provide a resolved phase measurement for thedistance estimation for the object.

In an embodiment, block 840 can includes blocks 840A and 840B.

At block 840A, calculate, by the at least one computing device, anupdated distance estimation for the object using the resolved phasemeasurement.

At block 840B, display, by a display device, at least one of theresolved phase measurement and the distance estimation.

At block 850, perform one or more actions based on at least one of theresolve phase measurement and the distance estimation. For example, theone or more actions can be directed to one or more of the following:object tracking; an Advanced Driver-Assistance System (ADAS);surveillance; and so forth.

FIG. 9 shows an exemplary method 900 for distance estimation between anRFID tag and an RFID reader, in accordance with an embodiment of thepresent principles.

At block 910, measure, by measurement equipment, a plurality of phasedifferences at different frequencies between transmitted RF signals fromthe RFID reader and corresponding received RF signals at the RFID tag.

At block 920, calculate, by the at least one computing device,normalized phases from the plurality of phase differences.

At block 930, calculate, by the at least one computing device, correctedphases by resolving one or more ambiguities from the normalized phases.

At block 940, obtain, by the at least one computing device, acharacteristic curve using the corrected phases.

At block 950, provide, by the at least one computing device, an estimateof the distance based on the characteristic curve and the correctedphases.

In an embodiment, block 950 can include block 950A.

At block 950A, display, by a display device, the estimate of thedistance.

At block 960, perform one or more actions based on the estimate of thedistance. For example, the one or more actions can be directed to one ormore of the following: object tracking; an Advanced Driver-AssistanceSystem (ADAS); surveillance; and so forth.

A description will now be given regarding various actions that can beperformed, in accordance with various embodiments of the presentinvention. The actions relate to steps 650, 750, 850, and 960 of methods600, 700, 800, and 900, respectively, as described with respect to FIGS.6, 7, 8, and 9, respectively.

Regarding object tracking, the one or more actions can include, but arenot limited to, one or more of the following: generate an image showingthe objects; provide a user-perceptible object tracking result (e.g., adistance estimate) to a user; perform one or more actions relating tothe distance estimate. In an embodiment, the user-perceptible objecttracking result can be in the form of a list of tracked objects which isdisplayed on a display device and/or provided through a speaker. Theactions that can be performed include, but are not limited to, canrelate to any of the following: object (person, pedestrian, animal,weapon, food, etc.) tracking; object tracking with respect to anapplication and so forth (e.g., retail (tracking customer path inshopping stores, airport or train station shopping malls), smarttransportation (tracking and regulating passenger or vehicle flow inairports, bus and train stations), security (monitor inmate separationdistances and so forth), safety (maintaining a predetermined distancefrom a dangerous object or condition)); ADAS (controlling vehiclefunctions including accelerating, braking, cruise control functions, andso forth); and so forth.

The one or more actions can be initiated by the corresponding at leastone computing device or another device, as readily appreciated by one ofordinary skill in the art, given the teachings of the present inventionprovided herein, while maintaining the spirit of the present invention.

A further description will now be given regarding various aspect of thepresent invention.

Herein, relative to one or more embodiments of the present invention,techniques are considered that rely on the power and phase of thereceived signal in order to estimate the distance. Using the phaseinformation allows us to potentially measure time-of-flight thatcorresponds to the time taken by the transmit wave to travel a distanceequivalent to its wavelength. Assuming that the wave travels to and fromthe object of interest in a given path, and the phase difference betweenthe transmitted and its corresponding signals is measured accurately atthe transmission point, the distance traveled by the wave would be somemultiples of the wavelength plus the fraction of the wavelength.Therefore, there is an inherent ambiguity associated with themeasurement since one cannot determine the exact number of wavelengthstravelled by the wave. Moreover, at a given frequency the transmit RFchain (including the antenna) and the receive RF chain (including theantenna) add a fixed, but unknown phase to the measurement. Thereflection off of the object also adds a fixed phase (usuallycorresponding to a half wavelength) to the measurement. Moreover, if thepath to and from the object includes some reflectors, there would bepotentially another additive phase that has to be accounted for in themeasurement.

Under these conditions, it is practically not possible to deduce anydistance information based on phase measurement at a single frequencyeven if the measurement is repeated over time. However, there is aninteresting way to find the distance if phase is measured at twodifferent frequencies. Let us assume that there is a single straightpath from the Measurement Equipment (ME) to the object of interest(OBJ). The measurement at each frequency can be interpreted asrepeatedly using a “ruler” of a size equal to the wavelength of thesignal to estimate the distance. However, the measurement does notreport how many times the ruler is used but only reports the finalfraction of the ruler size. If we use two different rulers (e.g., twodifferent wavelengths corresponding to two frequencies), then thedifference between the fractional length at the end can reveal valuableinformation about the actual distance without even knowing how manytimes each ruler is used.

In order to account for phase measurement inaccuracy, it is desirable touse multiple measurements at different frequencies. Using multiplefrequencies allows for resolving the ambiguities in the phasemeasurements as well. This ambiguity resolution may include finding thedifference between the number of times that the whole ruler is used inthe measurement of the distance. In other words, a first ruler may beused k₁ number of times with the fraction of the ruler remaining at theend that is equal to Ø₁ while a second ruler may be used k₂ number oftimes with the remaining fractional size of Ø₂. In general, we need toassume a relation between k₁ and k₂, e.g., k₁=k₂, in order to estimatethe distance based on Ø₁ and Ø₂, and it is not possible to resolve thisambiguity if we have only two frequencies. However, if multiple (morethan 2) frequencies are used, it would be possible to resolve suchambiguity, e.g., to deduce that k₂=k₁+1, in some cases. It will bediscussed herein after that there are certain intervals of length whereany distance in a given interval can be found uniquely based on thephase information if the phase information is accurate or its error isbounded by a given threshold. This phenomenon is referred to asuncertainty in distance estimation and such intervals are referred to asuncertainty regions. Hence, the accuracy of the distance estimationbased on measured phase has three different error types distinguished byambiguity, uncertainty, and resolution. The resolution depends on theerror in the measured phase and usually is modeled by a Gaussiandistribution as it is the case with thermal noise.

It is noted that there exists not only an inherent ambiguity in phaseestimation due to the fact that any factor of 2π can be subtracted fromor added to a phase without changing it, but also an explicit ambiguitymay occur due to the estimation procedure. Most software algorithms andhardware used in phase estimation depend on the arc tangent functionwhich causes a more ambiguous phase measurement with an ambiguity factorthat is equal to π or equivalently half a wavelength. Herein, analgorithm is provided that does not increase the ambiguity and provide aphase measurement with ambiguity factor of 2π. Moreover, the measuredphase is in fact a phase difference between the transmitted and itscorresponding received signals. Depending on which signal is consideredthe base, the sign of the phase difference (or phase shift) isdifferent. Thus, the distance estimation algorithm has to account forthe way that the phase difference is computed. In general, unless statedotherwise, we always assume that the transmit signal is considered as abase and the phase difference between the received signal in comparisonto the transmit signal is reported. Hence, if a hardware or softwarealgorithm considers the received signal as a base, we account for anegative sign in the phase measurement.

A description will now be given regarding distance estimation usingmulti-frequency phase measurement, in accordance with an embodiment ofthe present invention.

The idea of multi-frequency ruler for the purpose of distance estimationis expanded. Without loss of generality let us consider N measurementfrequencies f₁, f₂, f₃, . . . , f_(N) where f_(i)>f_(j) when i<j. Theassociated wavelengths λ_(i), i=1, . . . , N are given by

${\lambda_{i} = \frac{c}{f_{i}}},$where c is the speed of the light. Hence we have λ_(i)<λ_(j) when i<j.

Let us assume that the roundtrip distance between ME and OBJ is denotedby d. We note that in some situations, the distance between the twopoints might be found by transmission from a point, e.g., ME andreception at another point, e.g., OBJ and hence the distance drepresents only the one way path from ME to OBJ. The distance d can bewritten as d=k_(i)λ_(i)+Ø_(i) where Ø_(i)Ø[0, λ_(i)) and k_(i)∈

⁺∪{0} is anon-negative integer.

Hereinafter, we show that ϕ_(i) (or its corrected version ϕ̆_(i)) are anaffine function of λ_(i). Let us define a common integer factor ask=min_(i)k_(i) and define the corrected phaseϕ̆_(i)=ϕ_(i)+(k_(i)−k)λ_(i). Please note that with this definition, allϕ̆_(i) are nonnegative. The distance d can be written as d=kλ_(i)+ϕ̆_(i),∀_(i). Hence, we have the following:

$\begin{matrix}{k = \frac{{\overset{\Cup}{\phi}}_{i} - {\overset{\Cup}{\phi}}_{j}}{\lambda_{j} - \lambda_{i}}} & (1)\end{matrix}$while we note that since the phase measurements are not usuallyaccurate, the right hand side of Equation 1 has to be approximated withan integer, e.g., using a floor, ceiling, or round function. Thedifference of ϕ̆_(i)−ϕ̆_(j) in equation 1 is constant value k times thedifference between the corresponding wavelength values λ_(j)−λ_(i). Thisimplies that the relationship between the differential phase and thecorresponding differential wavelength is linear. Hence, the followingcan be written:ϕ̆_(i)=ϕ̆₀ +k(λ_(i)−λ₀)=ϕ̆₀ +kΔλ=(ϕ̆₀ −kλ ₀)+kλ _(i)  (2)for some constant values ϕ̆₀ and λ₀. This establishes the fact that thecorrected phase ϕ̆ is an affine function of λ.

This fact can be used to resolve the ambiguity of the phase estimationby transforming the estimates at different frequencies such that itscorresponding normalized phases follow a linear trend versus wavelength.We note that the actual measured phases θ are given by

$\theta_{i} = {\frac{2\pi{\overset{\Cup}{\phi}}_{i}}{\lambda_{i}} + {l\;\pi}}$for some ambiguity factor l. The ambiguity factor at least belongs tothe set of even integers since a measured phase has an inherentambiguity of any multiples of 2π. However, this ambiguity factor couldbelong to set of all possible integers (odd or even) for most practicalphase estimators since the state-of-the-art systems use arc tangentfunction, which has an ambiguity of any multiples of π. A phaseestimation procedure is proposed that allows for less ambiguity of equalto any multiples of 2π which is the best that one can hope for.

While we showed that the corrected normalized phases ϕ̆_(i) is an affinefunction of λ_(i), we note that the actual measured phase θ_(i) does notfollow the same property. In fact, we have the following:

$\begin{matrix}\begin{matrix}{\theta_{i} = {\frac{2\pi{\overset{\Cup}{\phi}}_{i}}{\lambda_{i}} + {l\;\pi}}} \\{= {\frac{2{\pi\left( {\left( {{\overset{\Cup}{\phi}}_{0} + {k\;\lambda_{0}}} \right) - {k\;\lambda_{i}}} \right)}}{\lambda_{i}} + {l\;{\pi(4)}}}} \\{= {\frac{2{\pi\left( \left( {{\overset{\Cup}{\phi}}_{0} + {k\;\lambda_{0}}} \right) \right)}}{\lambda_{i}} + {\left( {l - {2k}} \right)\;{\pi(5)}}}}\end{matrix} & (3)\end{matrix}$

This result means that the measured phase versus the wavelength followsa hyperbolic curve. This result enables the resolution of ambiguity forthe measured phase. The differential phase that is the differencebetween two measured phases θ_(i) and θ_(j) for the wavelength λ_(i) andλ_(j), respectively, can be found as follows:

$\begin{matrix}{{\theta_{i} - \theta_{j}} = {2{\pi\left( \left( {{\overset{\Cup}{\phi}}_{0} + {k\;\lambda_{0}}} \right) \right)}\left( {\frac{1}{\lambda_{i}} - \frac{1}{\lambda_{j}}} \right)}} & (6)\end{matrix}$

If the wavelengths are equally separated, i.e., λ_(i)=λ₀+iδλ, then wecan write the differential of the corrected normalized phases asfollows:ϕ̆_(i)−ϕ̆_(j) =k(j−i)δλ  (7)while for the measured phases θ_(i), the differential is given by thefollowing:

$\begin{matrix}{{\theta_{i} - \theta_{j}} = {2{\pi\left( \left( {{\overset{\Cup}{\phi}}_{0} + {k\;\lambda_{0}}} \right) \right)}\left( \frac{\left( {j - i} \right){\delta\lambda}}{\lambda_{i}\lambda_{j}} \right)}} & (8)\end{matrix}$which could be approximated by a linear function if δλ<<λ₀), and we havethe following:

$\begin{matrix}{{\theta_{i} - \theta_{j}} = {2{\pi\left( \left( {{\overset{\Cup}{\phi}}_{0} + {k\;\lambda_{0}}} \right) \right)}\left( \frac{\left( {j - i} \right){\delta\lambda}}{\lambda_{0}^{2}} \right)}} & (9)\end{matrix}$

The derivation in this section allows us to propose the followingsolution for the distance estimation based on the phase measurement.

In general, we can maximize the a posteriori probability of the distanced being equal to, e.g., d₀. A possible way is to consider GLRT(Generalized Maximum Likelihood Ratio Test). Assuming that thedistribution of the measurement is known, one can formulate the problemas follows:

$\begin{matrix}{\max\limits_{k,d}{p\left( {\Theta,k,d} \right)}} & (10)\end{matrix}$where p(Θ, k, d) is the probability distribution of the vector ofmeasured phases Θ=[θ₁, θ₂, . . . , θ_(N)], k is the common integerfactor, and d is the distance of OBJ from ME. The problem can also bestated in terms of vector of the corrected normalized phases Φ̆=[ϕ̆₁, ϕ̆₂,. . . , ϕ̆_(n)] as follows:

$\begin{matrix}{\max\limits_{k,d}{p\left( {\overset{\Cup}{\Phi},k,d} \right)}} & (11)\end{matrix}$where p (Φ̆, k, d) is the joint probability distribution of the vector ofcorrected normalized phases. For example assuming that this distributionis Gaussian (and independent across frequencies), we have the following:

$\begin{matrix}{{\max\limits_{k,d}{p\left( {\overset{\Cup}{\Phi},k,d} \right)}} = {\max\limits_{k,d}{\prod\limits_{i = 1}^{N}\;{\frac{1}{\sqrt{2{\pi\sigma}^{2}}}{\exp\left( {\frac{- 1}{2\sigma^{2}}\left( {\phi_{i} - d - {k\;\lambda_{i}}} \right)^{2}} \right)}}}}} & (12)\end{matrix}$

This corresponds to the following:

$\begin{matrix}{\min\limits_{k,d}{\sum\limits_{i = 1}^{N}\;\left( {\phi_{i} - d - {k\;\lambda_{i}}} \right)^{2}}} & (13)\end{matrix}$

Taking the derivative with respect to d we have the following:

$\begin{matrix}{d = {{\frac{k}{N}{\sum\limits_{i = 1}^{N}\;\lambda_{i}}} + {\frac{1}{N}{\sum\limits_{i = 1}^{N}\;\phi_{i}}}}} & (14)\end{matrix}$and taking the derivative with respect to k (treating k as a real numberand then digitizing it, e.g., by using a round function), we have thefollowing:kΣ _(i=1) ^(N)λ_(i) ²+Σ_(i=1) ^(N)λ_(i)(ϕ_(i) −d)=0  (15)

Hence, we can approximate k by the following:

$\begin{matrix}{k = {{round}\frac{\sum\limits_{i = 1}^{N}\;{\lambda_{i}\left( {\phi_{i} - d} \right)}}{\sum\limits_{i = 1}^{N}\;\lambda_{i}^{2}}}} & (16)\end{matrix}$

The last two equations give complete solution for the distance based onthe set of the measured phases at different wavelengths.

We note that if the correction of the phases have not happened before,the above formulation and solution cannot work for the correctednormalized phases and the original problem and

$\begin{matrix}{\max\limits_{k,d}{p\left( {\Theta,k,d} \right)}} & (17)\end{matrix}$has to be solved under the constraint that the vector of Θ follow ahyperbolic curve denoted for example by Equation (6) or any simplifiedversion of it such as Equations (8) or (9).

One possible approach is to first resolve the ambiguity and then use thecorrected normalized phases to find the distance estimate. Hence, as afirst step after gathering the phase information, we need to resolve theambiguities. The ambiguities for the measured phases could be resolvedby considering the fact that all the measured phases lie on a hyperbola.Therefore, the noisy version of the data should follow the bestapproximation of a hyperbola. In some cases, the hyperbola can beapproximated with linear function. Another possibility is to find theuncorrected normalized phase values by multiplying each θ_(i) by itswavelength λ (and divide the result by 2π). These uncorrected normalizedphases versus wavelength should be lying on a straight line and thisproperty can be used to resolve the ambiguity.

After the step of ambiguity resolution, one can directly use thesolution in Equations (14) and (16) to find the distance estimate. Theother way is to find the slope of the line for the corrected normalizedphases and use the following equation d=ϕ̆_(i)+kλ_(i). We note that thesolution of k in this approach could be a real number in general and itsatisfies some optimality constraint. On the other hand one may add astep of digitizing the value of k, e.g., by rounding it to the nearestinteger. We also note that if the ambiguity resolution step is performedon the vector of the measured phases directly, then the correctedmeasured phases have to be modified to get the corrected normalizedphases before finding the slope of the line. This step may also beignored in some cases, depending upon the implementation.

A description will now be given regarding resolving the ambiguity of themeasured phases, in accordance with an embodiment of the presentinvention.

First Observation: Resolving the ambiguity of the measured phases relieson the (first) observation that if the OBJ is not moving and d isconstant (or almost constant), the corrected normalized phases follow aparticular trend. This means that the corrected normalized phases versusthe wavelength is an affine function, hence, it has two unknownparameters, i.e., the value of the function at a given wavelength andthe slope of the line. However, in practical cases, the measured phasesare noisy, hence, although this linear trend exists, it is approximate.Once the ambiguity is resolved it is easy to use different algorithms tocome up with the optimal slope. For example, a least squared algorithmfinds a line passing through all points (corrected normalized phasesversus wavelength) which has the minimum squared error for all thepoints. Other algorithms may rely on GLRT, MAP (Maximum a posteriori),or ML (Maximum Likelihood) to find the slope.

Second Observation: The main question is how to generate the correctednormalized phases. A second observation is that the measured phasesand/or normalized phases are only meaningful if an ambiguity resolutionprocedure exists that, for example, takes the measured phases ornormalized phases as an input and generates corrected normalized phasesor corrected measured phases such that they follow a linear orhyperbolic trend, respectively. Stated otherwise, the noise or themeasurement error should be within a reasonable threshold that it doesnot mask this trend. Therefore, an optimization algorithm to resolve theambiguity looks for all variations of the normalized phases that can bevalid based on the measured phases. To generate all variations, one hasto consider adding any integer multiples of lπ (based on the ambiguityfactor l) to the measured phases. It also includes adding all possiblemultiples of 2kπ to normalized measured phases. Among all suchvariations for all the measured phases, the optimized algorithm shouldpick the corrected normalized phases as the ones that have the leasterror in realizing the linear trend for the selected correctednormalized phases. Such algorithm is very exhaustive even if we limitthe number of variations by considering a finite multiples of theambiguity factors.

Hereinafter, a two-step approach is provided for ambiguity resolution asfollows: (1) an intra-frequency ambiguity resolution; and (2) aninter-frequency ambiguity resolution. In the first step, we combine allthe information gathered for a specific wavelength into a representativegroup. This algorithm can be viewed as a classification algorithm with aconstraint on the representatives of the classes. For example, for eachclass, consider the mean of all the members of the class and the definethe error to be the distance between this mean value and therepresentative of the class. The constraint may be stated as having thesum of squared error to be less than a threshold. Alternatively, we candefine this sum of squared errors as the objective function and minimizethis to find the classes. Another example of the error function could bethe sum of squared error between each member of the class to the classrepresentative. The sum of all such errors can again be used as anobjective function to minimize and find the classes. These classes arethen combined into a single group by adding appropriate integermultiples of the ambiguity factor for each class. It is noted that eachclass should satisfy a figure of merit (FoM), where FoM has to be abovea certain (first) threshold for the class to be acceptable. Otherwise,the algorithm can have a decision that below a certain (second)threshold (may be different form the first threshold) for a class, thisclass is rejected or it is declared that the OBJ is moving or themeasurement environment is not stationary.

In the second step of the algorithm, the first observation is used,i.e., the fact that the corrected normalized phases have to follow atrend (up to the measurement error) of an affine function. It is notedthat the first step of the algorithm provides a group or measurement setfor each wavelength where the intra-frequency ambiguity among the phaseshave been supposedly resolved. The first step of the algorithm can alsoprovide the assumed representative computed in the first step for thisgroup or a new representative, e.g., the mean or median of the group,may be generated. These representatives can be used to resolve theinter-frequency ambiguity by adding multiples of the ambiguity factor,e.g., π, to the representative of each group such that the new correctednormalized values for the representatives follows a straight lineclosely. In a more precise statement, this means that the objectivevalue of the lease squared solution for the set of corrected normalizedrepresentatives versus wavelength is minimized.

A simple procedure for the second step is as follows. We start from thesmallest wavelength and work though each wavelength sequentially to thelargest. For each wavelength except the first one, we consider adding amultiple of the ambiguity factor such that the resulting phase is largerthan that of the previous wavelength but the difference is less than athreshold. This threshold may depend on the frequency spacing orequivalently wave-length spacing. In particular, if all wavelengths areequally separated, then only one threshold may be used. An example ofthis threshold is equal to the ambiguity factor. This means that everytwo consecutive corrected phases are not more than an ambiguity factorapart and the corrected normalized phase versus wavelength isnon-decreasing. We note that this procedure is especially more efficientif the wavelengths are equally separated. Since the slope and they-intercept of the line passing through the corrected normalized phasesdetermines the distance d between OBJ and ME, the threshold on thedifference between two corrected normalized phases for two consecutivewavelength λ_(i) and λ_(i+1) determines the maximum possible slope thata characteristic curve (the line in this case) can have and it isdetermined by the ratio of the ambiguity factor to δλ defined asδλ=λ_(i+1)−λ_(i).

This gives a limit to the maximum distance that multi-frequency distanceestimation can uniquely identify. This maximum distance is also referredto as the certainty distance. The uncertainty in the distance estimationstates that any distance beyond this distance cannot be uniquelydetermined based on the measured phases. We note that the certaintydistance cannot be made arbitrarily large by reducing the differencebetween consecutive wavelength δλ, since the principle of ambiguityresolution depends on the first and second observations describedearlier, where the variance of the error or noise in phase measurementshould not mask the possibility of distinguishing the characteristiccurve with a reasonably small error. Therefore, the limiting factor isthe error in the phase measurement.

A description will now be given regarding intra-frequency ambiguityresolution, in accordance with an embodiment of the present invention.

Consider a set of measured phases S_(i) for a given wavelength λ_(i). Wewould like to find a solution for the following optimization problem:

$\begin{matrix}{\min\limits_{{r{(s)}}R_{i}}{\sum\limits_{s \in S_{i}}\;{m\left( {s,{r(s)}} \right)}}} & (18) \\{{S.t.\mspace{14mu}{\forall r_{1}}},{{r_{2} \in {{R_{i}r_{1}} - r_{2}}} = {{kl}\;\pi}},{\exists{k \in {Z -}}}} & (19)\end{matrix}$where m(s,r(s)) denote a distance measure between s and r(s), e.g.,m(s,r(s))=(s−r(s))², and R_(i) is a set of representative for thewavelength λ_(i), and r(s) is a function that maps every points in themeasurement set S_(i) to one of the points in the representative setR_(i). This formulation can be interpreted as partitioning the set ofmeasured phases S_(i) and assigning one representative to each partitionand considering an error measure or distance measure that finds the sumof the errors (or distances) between the values in each partition andits representative. The constraint specifies that the representativeshave to be separated by integer multiples of the ambiguity factor lπ.

A possible approach to solve this problem is to consider a threshold,e.g., tlπ, for some t∈(0, 1). Going through all the points in set S_(i),we generate a new partition if the absolute distance between the newpoint and all previously considered points is more than this threshold,and we put the new point into a previously formed partition if theabsolute distance between this point and one of the points (or therepresentative of the partition) is less than this threshold. For thefirst point, we just make a new partition with that point. For low tomoderate measurement error, this algorithm is always converging to theoptimal solution. However, for a large measurement error, solving theabove optimization problem directly gives a better answer.

After partitioning the set S_(i), and finding the representative setR_(i), one needs to merge these partitions into one group by addingappropriate multiples of the ambiguity factor lπ into each group. Theresult will be a group of points for which the absolute distance shouldnot exceed the ambiguity factor lπ. If there is no set of integermultiples that can provide such a solution, then the system can declarethat the OBJ is moving or the measurement environment is not stationary.Of course, another reason could be that the measurement error itself istoo large. We note that by definition this would never happen for theoptimal solution since the optimal solution finds the partitions suchthat their representatives are always integer multiples of the ambiguityfactor lπ apart and, hence, it is always possible to subtract thecorresponding integer multiple of the ambiguity factor to reach to agroup of points that are never more than lπ apart. However, this couldhappen for the proposed suboptimal solution that performs thepartitioning by one pass operation over all the points in the set ofmeasured phases S_(i).

It is always possible to consider a second threshold t₂lπ, for somet₂∈(0, 1) such that if the absolute distance between the data in thefinal group exceeds this threshold, the system can declare sensingmovement or anon-stationary environment. We note that in a practicalsetting usually t₂≥t. The larger the value of t, the larger measurementerror that can be handled by the proposed solution. However, it is notrecommended to use any value greater than one half for t.

The Intra-frequency ambiguity resolution not only is an essential stepto generate a meaningful phase reading at each wavelength, but also itprovides a means to detect movement of the OBJ or other objects invicinity of the reader.

A description will now be given regarding inter-frequency ambiguityresolution, in accordance with an embodiment of the present invention.

The output of the previous step, i.e., intra-frequency ambiguityresolution is N groups of measurements for each frequency, e.g., G₁, G₂,. . . , G_(N). The optimization problem which to find the distance canbe now stated in terms of vector all corrected normalized phases in allgroups g=[g₁₁, g₁₂, . . . , g₂₁, g₂₂, . . . ], where g_(ij) is thej^(t)h element of the group i, as follows:

$\begin{matrix}{\max\limits_{k,d}{p\left( {g,k,d} \right)}} & (20)\end{matrix}$

One can potentially finds a representative r_(i) for each group and forma vector r=[r₁, r₂, . . . , r_(N)] and write the optimization problem asfollows:

$\begin{matrix}{\max\limits_{k,d}{p\left( {r,k,d} \right)}} & (21)\end{matrix}$

A suboptimal but efficient solution for this problem can be found whenthe joint probability distribution function is Gaussian. As discussedpreviously, we note that if the transmit signal is considered as a basefor the purpose of differential phase measurement, then the larger thewavelength, the smaller the corrected differential phase. This situationis reversed if the received signal is considered as a base for thepurpose of differential phase measurement. In the latter case, thelarger the wavelength, the larger the corrected differential phases. Ineither scenario, a simple yet efficient algorithm may be used forinter-frequency ambiguity resolution such that for each pair ofconsecutive wavelengths, we resolve the ambiguity by adding appropriatemultiples of the ambiguity factor lπ such that |r_(i+1)−r_(i)|<lπ. Thismeans that in the former scenario −lπ<r_(i+1)−r_(i)≤0 and in the lattercase 0≤r_(i+1)−r_(i)<lπ. Then, the slope of the resulting curve (or theslope of the least square solution for the corrected normalized phases)is equal to the common integer factor k described earlier. The estimateddistance can be then found as d=kλ_(i)+ϕ̆_(i) or equivalentlyd=kλ_(i)+r_(i).

A description will now be given regarding the received signal at themeasurement equipment (ME), in accordance with an embodiment of thepresent invention.

When a signal is generated by the measurement equipment (ME) andtransmitted over the air, there are multiple ways that the return signalfrom an object of interest (OBJ) could be generated and measured at ME.One possible scenario is the case that the reflection from OBJ isreceived by ME. This scenario may include a multi-path channel where,for each path, the transmitted signal from ME to OBJ and/or thereflected signal from OBJ to ME might be reflected off of some otherobjects. The other scenario is the case that OBJ itself receives thetransmitted signal from ME (again possibly through multi-path channel)and after processing the signal OBJ, replies back with another signalthat is then received by ME (also possibly through multi-path). Thislatter scenario include the cases that the processing is a simplebackscattering modulation of the signal received by OBJ, e.g., in RFIDsystems.

It should be noted that it is possible to reduce the effect ofmulti-path and possible reflections off of some object by usingpolarization. One possible way is to use right handed (RH) circularlypolarized (RHCP) transmit waves. In this case, the round-trip path withan odd number of reflections will be received back at ME as invertedpolarization, i.e., a left handed (LH) circularly polarized (LHCP) wave,whereas the round-trip path with an even number of reflections will bereceived with similar polarization as the transmitted signal, i.e.,RHCP. Depending on the scenario, one or the other polarization may beignored. For example, for the systems that rely on the reflection off ofOBJ, the inverted polarization will be used and the part of receivedsignal with similar polarization will be ignored. The reason is that thedirect path has only one reflection, i.e., an odd reflection and thedistance depend on the direct path. In general, the higher the number ofreflections, the lower the gain associated with that path. Hence, allthe second order paths with only two reflections are ignored and thestrongest interference will come from all third order paths with threereflections in their round-trip path, and the third order paths ingeneral have lower average energy than the second order paths.

In the other scenario, where OBJ generates a reply and sends it back, wecan only detect signals with even polarization, and ignore the componentof the signal with odd polarization. It is to be noted that this dependon the fact that OBJ only uses linear polarization instead of circularpolarization for its reply. The fact that odd polarization is ignoredrelates to the fact that we would like to minimize the contribution ofreflections from different objects and possibly including OBJ since thereflections are only interference in this case and the signal to bemeasured is the reply signal from OBJ. We note that the overallcontribution of the odd polarization signal in the received signal at MEis more than the contribution of the even polarized signal due to theaforementioned fact about the reduction of the path gain when the numberof the number of reflections in the path increases. However, since thereply from OBJ is linearly polarized, it can be received and detected bythe receive RF chain (the circuit and antenna) at ME.

Embodiments described herein may be entirely hardware, entirely softwareor including both hardware and software elements. In a preferredembodiment, the present invention is implemented in software, whichincludes but is not limited to firmware, resident software, microcode,etc.

Embodiments may include a computer program product accessible from acomputer-usable or computer-readable medium providing program code foruse by or in connection with a computer or any instruction executionsystem. A computer-usable or computer readable medium may include anyapparatus that stores, communicates, propagates, or transports theprogram for use by or in connection with the instruction executionsystem, apparatus, or device. The medium can be magnetic, optical,electronic, electromagnetic, infrared, or semiconductor system (orapparatus or device) or a propagation medium. The medium may include acomputer-readable medium such as a semiconductor or solid state memory,magnetic tape, a removable computer diskette, a random access memory(RAM), a read-only memory (ROM), a rigid magnetic disk and an opticaldisk, etc.

It is to be appreciated that the use of any of the following “/”,“and/or”, and “at least one of”, for example, in the cases of “A/B”, “Aand/or B” and “at least one of A and B”, is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of both options (A andB). As a further example, in the cases of “A, B, and/or C” and “at leastone of A, B, and C”, such phrasing is intended to encompass theselection of the first listed option (A) only, or the selection of thesecond listed option (B) only, or the selection of the third listedoption (C) only, or the selection of the first and the second listedoptions (A and B) only, or the selection of the first and third listedoptions (A and C) only, or the selection of the second and third listedoptions (B and C) only, or the selection of all three options (A and Band C). This may be extended, as readily apparent by one of ordinaryskill in this and related arts, for as many items listed.

Having described preferred embodiments of a system and method (which areintended to be illustrative and not limiting), it is noted thatmodifications and variations can be made by persons skilled in the artin light of the above teachings. It is therefore to be understood thatchanges may be made in the particular embodiments disclosed which arewithin the scope and spirit of the invention as outlined by the appendedclaims. Having thus described aspects of the invention, with the detailsand particularity required by the patent laws, what is claimed anddesired protected by Letters Patent is set forth in the appended claims.

What is claimed is:
 1. A system for resolving ambiguity in a phase measurement used in a distance estimation for an object, comprising: a transmitter for transmitting RF signals from a location of the object; measurement equipment, including a receiver, for receiving the transmitted RF signals as corresponding received RF signals and measuring a plurality of phases at different frequencies between the transmitted RF signals and the corresponding received RF signals; a processor configured to calculate normalized phases from the plurality of measured phases; perform an intra-frequency ambiguity resolution process that resolves an ambiguity for the normalized phases for a single frequency using an ambiguity factor; and perform an inter-frequency ambiguity resolution process that resolves an ambiguity for the normalized phases across a plurality of tones using a characteristic curve to provide a resolved phase measurement for the distance estimation for the object.
 2. The system of claim 1, wherein the transmitted RF signals are transmitted using a plurality of wavelengths, and wherein the intra-frequency ambiguity resolution process comprises generating a single representative group of corrected phases for a metric selected from the group consisting of a given one of the different frequencies and a given one of the plurality of wavelengths.
 3. The system of claim 2, wherein a spread of the single representative group is defined as a maximum difference between group members of the single representative group, and wherein the phase measurement is valid when the spread is less than a threshold.
 4. The system of claim 2, wherein a spread of the single representative group is defined as a maximum difference between group members of the single representative group, and wherein the spread is used to determine a non-stationary environment.
 5. The system of claim 2, wherein a spread of the single representative group is defined as a maximum difference between group members of the single representative group, and wherein the spread is used to determine a status of the object from among statuses selected from the group consisting of static and moving.
 6. The system of claim 1, wherein the transmitted RF signals are transmitted using a plurality of wavelengths, and wherein the intra-frequency ambiguity resolution process comprises partitioning the normalized phases for a metric selected from the group consisting of a given one of the plurality of wavelengths and a given one of the different frequencies into one or more classes such that (a) a representative phase from among the normalized phases is associated with a class and (b) a difference between two representative phases from among the normalized phases is an integer multiple of the ambiguity factor.
 7. The system of claim 6, wherein the ambiguity factor is equivalent to a value selected from the group consisting of 2π and π.
 8. The system of claim 6, wherein a distance measure between the representative phase and members of its class is minimized.
 9. The system of claim 6, wherein the one or more classes are generated by adding a normalized phase to a class if a distance of the normalized phase from other members of a same one of the one or more classes is less than a threshold, and wherein a new class is generated when the distance of the normalized phase from members of all of the one or more classes is more than a threshold.
 10. The system of claim 9, wherein at least two classes from among the one or more classes and the new class are merged into a single group by adding an integer multiple of the ambiguity factor to at least one member of the at least two classes.
 11. The system of claim 1, wherein the inter-frequency ambiguity resolution process is performed by adding a same integer multiple of the ambiguity factor to a member of at least one group to generate a corrected group.
 12. The system of claim 11, wherein the adding the same integer multiple of the ambiguity factor to a member of at least one group is performed such that resulting group members follow a characteristic curve.
 13. The system of claim 11, wherein the transmitted RF signals are transmitted using a plurality of wavelengths, and wherein a maximum distance between the normalized phases of members of the corrected group for two consecutive ones of the plurality of wavelengths is less than the ambiguity factor.
 14. The system of claim 11, wherein a characteristic error that is a sum of mean squared difference between the members of corrected group and the characteristic curve is minimized.
 15. The system of claim 14, wherein the characteristic error is used to determine a nonstationary environment.
 16. The system of claim 14, wherein the characteristic error is used to determine a status of the object from among statuses selected from the group consisting of static and moving.
 17. The system of claim 1, wherein the transmitted RF signals are transmitted using a plurality of wavelengths, and wherein the characteristic curve, relating to the normalized phases versus the plurality of wavelengths, is a function selected from a group of functions consisting of an affine function and a hyperbolic function.
 18. The system of claim 1, wherein the plurality of frequencies are Orthogonal Frequency Division Multiplexing (OFDM) tones in an OFDM system.
 19. A computer-implemented method for resolving ambiguity in a phase measurement used in a distance estimation for an object, comprising: measuring, by measurement equipment, a plurality of phases at different frequencies between transmitted Radio Frequency (RF) signals from a location of the object and corresponding received RF signals at the measurement equipment; calculating, by a processor, normalized phases from the plurality of measured phases; performing, by the processor, an intra-frequency ambiguity resolution process that resolves an ambiguity for the normalized phases for a single frequency using an ambiguity factor; and performing, by the processor, an inter-frequency ambiguity resolution process that resolves an ambiguity for the normalized phases across a plurality of tones using a characteristic curve to provide a resolved phase measurement for the distance estimation for the object.
 20. A computer program product for resolving ambiguity in a phase measurement used in a distance estimation for an object, the computer program product comprising a non-transitory computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computer to cause the computer to perform a method comprising: measuring, by measurement equipment, a plurality of phase differences at different frequencies between transmitted Radio Frequency (RF) signals from a location of the object and corresponding received RF signals at the measurement equipment; calculating, by a processor, normalized phases from the measured phases; performing, by the processor, an intra-frequency ambiguity resolution process that resolves an ambiguity for the normalized phases for a single frequency using an ambiguity factor; and performing, by the processor, an inter-frequency ambiguity resolution process that resolves an ambiguity for the normalized phases across a plurality of tones using a characteristic curve to provide a resolved phase measurement for the distance estimation for the object. 